static double RunTest
(enum CBLAS_ORDER Order, enum TEST_UPLO Uplo, int N, int lda,
int CacheSize, TYPE *res)
{
TYPE *A, *AI, *C;
int ierr;
double t0, t1;
A = GetMat(Order, Uplo, N, lda);
#ifdef DEBUG
Mjoin(PATL,geprint)("A0", N, N, A, lda);
#endif
AI = DupMat(Order, N, N, A, lda, lda);
t0 = ATL_flushcache(CacheSize);
t0 = ATL_flushcache(-1);
t0 = time00();
test_inv(Order, Uplo, N, AI, lda); /* AI should now have inverse(A) */
t1 = time00() - t0;
t0 = ATL_flushcache(0);
#ifdef DEBUG
Mjoin(PATL,geprint)("A ", N, N, A, lda);
Mjoin(PATL,geprint)("AI", N, N, AI, lda);
#endif
*res = GetResid(Order, Uplo, N, A, lda, AI, lda);
free(AI);
free(A);
return(t1);
}
static double RunTiming
(enum CBLAS_ORDER Order, enum TEST_UPLO Uplo, int N, int lda,
int CacheSize, int nreps)
{
TYPE *A, *a;
const int incA = N*lda;
int i, k;
double t0, t1=0.0;
if (nreps < 1) nreps = 1;
i = ATL_DivBySize(2*CacheSize) ATL_PTCACHEMUL;
k = i = (i + N*N-1) / (N*N);
if (nreps > i) k = i = nreps;
a = A = malloc(i * ATL_MulBySize(incA));
if (A)
{
if (Uplo == TestGE)
for (i=0; i < k; i++) Mjoin(PATL,gegen)(N, N, A+i*incA, lda, N+lda);
else for (i=0; i < k; i++) hegen(Order, Uplo, N, A+i*incA, lda);
t0 = time00();
for (i=nreps; i; i--, a += incA) test_inv(Order, Uplo, N, a, lda);
t1 = time00() - t0;
free(A);
}
else fprintf(stderr, " WARNING: not enough mem to run timings!\n");
return(t1/nreps);
}
double GetTimeWithReps_LU
(int mflopF, int lda, int M, int N, int nb, int Uplo, int Side, int flsizeKB)
{
double mflop, t0, t1, drep;
char *wrksets; /* working sets for kernel calls */
#ifdef TCPLX
const int lda2 = lda+lda;
#else
const int lda2 = lda;
#endif
size_t setsz, setszT; /* work set size in memory, and amnt of it touched */
size_t nrep; /* # of reps required to force mflopF flops */
size_t nset; /* # of working sets allocated */
int i;
/*
* Keep setsz a multiple of TYPE size for alignment reasons. LU only accesses
* M*N of matrix and all of IPIV.
*/
setsz = lda*N*ATL_sizeof +
((M*sizeof(int)+ATL_sizeof-1)/ATL_sizeof)*ATL_sizeof;
setszT = M*N*ATL_sizeof + M*sizeof(int);
mflop = GetFlopCount(LAgetrf, 0, M, N, 0, 0, CAN_NB);
/*
* Cannot reuse matrices (bogus to factor an already factored matrix), so we
* must take as our total memspace MAX(nrep,nset)*setsz
*/
ATL_assert(mflop > 0.0);
drep = (mflopF*1.0e6) / mflop;
nrep = (int)(drep+0.999999);
/*
* If cacheline flush doesn't work, then we must use this method
*/
#if ATL_LINEFLUSH
if (nrep < 2)
return(-1.0); /* do wt normal timer */
#else
nrep = (nrep >= 1) ? nrep : 1;
#endif
nset = (flsizeKB*1024+setszT-1)/setszT;
if (nset < nrep)
nset = nrep;
wrksets = malloc(nset * setsz);
ATL_assert(wrksets);
for (i=0; i < nset; i++)
Mjoin(PATL,gegen)(M, N, (TYPE*)(wrksets+i*setsz), lda, M*N+lda);
t0 = time00();
for (i=0; i < nrep; i++)
{
test_getrf(CblasColMajor, M, N, (TYPE*)(wrksets+i*setsz), lda,
(int*)(wrksets+i*setsz+lda*N*ATL_sizeof));
}
t1 = time00();
free(wrksets);
return((t1-t0)/((double)nrep));
}
int RunCase(int CacheSize, TYPE thresh, int MFLOP, enum ATLAS_ORDER Order,
enum ATLAS_UPLO Uplo, int N, int lda)
{
char *Ups, *Ord;
TYPE resid = 0.0;
double mflop, mflops, t0, tim=0.0;
int nreps=1, passed, i, imem;
const int incA = lda*N;
TYPE *a, *A;
mflops = N;
mflops = (mflops*mflops*mflops) / 4.0;
#ifdef TCPLX
mflops *= 4.0;
#endif
mflops /= 1000000.0;
if (thresh > ATL_rzero) resid =
uumtest(Order, Uplo, CacheSize, N, lda, &tim);
else resid = -1.0;
if (MFLOP > mflops || thresh <= ATL_rzero) /* need to time repetitively */
{
nreps = (mflops * 1000000);
nreps = (MFLOP*1000000 + nreps-1) / nreps;
if (nreps < 1) nreps = 1;
imem = ATL_DivBySize(CacheSize) ATL_PTCACHEMUL;
imem = (imem + 2*N*N-1) / (N*N);
if (imem < nreps) imem = nreps;
a = A = malloc(imem * ATL_MulBySize(incA));
if (A != NULL)
{
for (i=0; i < imem; i++) lltgen(Uplo, N, A+i*incA, lda, N*1029+lda);
t0 = time00();
for (i=nreps; i; i--, a += incA)
test_lauum(Order, Uplo, N, a, lda);
tim = time00() - t0;
tim /= nreps;
free(A);
}
else fprintf(stderr, " WARNING: not enough mem to run timings!\n");
}
if (tim > 0.0) mflop = mflops / tim;
else mflop = 0.0;
if (Uplo == AtlasUpper) Ups = "Upper";
else Ups = "Lower";
if (Order == CblasColMajor) Ord = "Col";
else Ord = "Row";
fprintf(stdout, "%5d %3s %5s %6d %6d %12.5f %12.3f %12e\n",
nreps, Ord, Ups, N, lda, tim, mflop, resid);
if (resid > thresh || resid != resid) passed = 0;
else if (resid < 0.0) passed = -1;
else passed = 1;
return(passed);
}
static TYPE lutestR(int CacheSize, int M, int N, int lda, int *npiv,
double *tim)
{
TYPE *A, *LmU;
int *ipiv;
const int MN = Mmin(M,N);
int i;
double t0, t1;
TYPE normA, eps, resid;
eps = Mjoin(PATL,epsilon)();
A = malloc(ATL_MulBySize(lda)*M);
if (A == NULL) return(-1);
ipiv = malloc( MN * sizeof(int) );
if (ipiv == NULL)
{
free(A);
return(-1);
}
t0 = ATL_flushcache(CacheSize);
Mjoin(PATL,gegen)(N, M, A, lda, M*N+lda);
#ifdef DEBUG
Mjoin(PATL,geprint)("A0", N, M, A, lda);
#endif
normA = Mjoin(PATL,genrm1)(N, M, A, lda); /* actually infnrm, but OK */
t0 = ATL_flushcache(-1);
t0 = time00();
test_getrf(CblasRowMajor, M, N, A, lda, ipiv);
t1 = time00() - t0;
*tim = t1;
t0 = ATL_flushcache(0);
#ifdef DEBUG
Mjoin(PATL,geprint)("LU", N, M, A, lda);
#endif
LmU = ATL_LmulUR(M, N, A, lda); /* LmU contains L * U */
#ifdef DEBUG
Mjoin(PATL,geprint)("L*U", N, M, LmU, N);
#endif
Mjoin(PATL,gegen)(N, M, A, lda, M*N+lda); /* regenerate A, overwriting LU */
ATL_laswp(M, A, lda, 0, MN, ipiv, 1); /* apply swaps to A */
resid = Mjoin(PATL,gediffnrm1)(N, M, A, lda, LmU, N);
resid /= (normA * eps * Mmin(M,N));
*npiv = findnpvt(MN, ipiv);
free(LmU);
free(A);
free(ipiv);
return(resid);
}
static TYPE uumtest(enum ATLAS_ORDER Order, enum ATLAS_UPLO Uplo,
int CacheSize, int N, int lda, double *tim)
{
TYPE *A, *Ag, *LmLt;
double t0, t1;
TYPE normA, eps, resid;
enum ATLAS_UPLO MyUplo = Uplo;
if (Order == CblasRowMajor)
{
if (Uplo == CblasUpper) MyUplo = CblasLower;
else MyUplo = CblasUpper;
}
eps = Mjoin(PATL,epsilon)();
A = malloc(ATL_MulBySize(lda)*N + ATL_MulBySize(N)*N);
if (A == NULL) return(-1);
Ag = A + lda*(N SHIFT);
t0 = ATL_flushcache(CacheSize);
lltgen(MyUplo, N, A, lda, N*1029+lda);
lltgen(MyUplo, N, Ag, N, N*1029+lda);
normA = lltnrm1(MyUplo, N, A, lda);
#ifdef DEBUG
Mjoin(PATL,geprint)("A", N, N, A, lda);
Mjoin(PATL,geprint)("Ag", N, N, Ag, N);
#endif
t0 = ATL_flushcache(-1);
t0 = time00();
test_lauum(Order, Uplo, N, A, lda);
t1 = time00() - t0;
*tim = t1;
t0 = ATL_flushcache(0);
ATL_checkpad(MyUplo, N, A, lda);
if (Uplo == CblasUpper) LmLt = ATL_UmulUt(Order, N, Ag, N);
else LmLt = ATL_LtmulL(Order, N, Ag, N);
#ifdef DEBUG
Mjoin(PATL,geprint)("A", N, N, A, lda);
Mjoin(PATL,geprint)("Ag", N, N, LmLt, N);
#endif
lltdiff(MyUplo, N, A, lda, LmLt, N);
#ifdef DEBUG
Mjoin(PATL,geprint)("A-L*Lt", N, N, LmLt, N);
#endif
resid = lltnrm1(MyUplo, N, LmLt, N) / (normA * eps * N);
if (resid > 10.0 || resid != resid)
fprintf(stderr, "normA=%e, eps=%e, num=%e\n", normA, eps, resid);
free(LmLt);
free(A);
return(resid);
}
double GetTimeWithReps_LLT
(int mflopF, int lda, int M, int N, int nb, int Uplo, int Side, int flsizeKB)
{
double mflop, t0, t1, drep;
char *wrksets; /* working sets for kernel calls */
#ifdef TCPLX
const int lda2 = lda+lda;
#else
const int lda2 = lda;
#endif
size_t setsz, setszT; /* work set size in memory, and amnt of it touched */
size_t nrep; /* # of reps required to force mflopF flops */
size_t nset; /* # of working sets allocated */
int i;
setsz=lda*N*ATL_sizeof; /* matrix is entire working set of LLt */
setszT=N*N*ATL_sizeof; /* only touch N*N portion */
mflop = GetFlopCount(LApotrf, Uplo, M, N, 0, 0, CAN_NB);
/*
* Cannot reuse matrices (bogus to factor an already factored matrix), so we
* must take as our total memspace MAX(nrep,nset)*setsz
*/
ATL_assert(mflop > 0.0);
drep = (mflopF*1.0e6) / mflop;
nrep = (int)(drep+0.999999);
/*
* If cacheline flush doesn't work, then we must use this method
*/
#if ATL_LINEFLUSH
if (nrep < 2)
return(-1.0); /* do wt normal timer */
#else
nrep = (nrep >= 1) ? nrep : 1;
#endif
nset = (flsizeKB*1024+setszT-1)/setszT;
if (nset < nrep)
nset = nrep;
wrksets = malloc(nset * setsz);
ATL_assert(wrksets);
for (i=0; i < nset; i++)
PosDefGen(CblasColMajor, Uplo_LA2ATL(Uplo), N,
(TYPE*)(wrksets+i*setsz), lda);
t0 = time00();
for (i=0; i < nrep; i++)
{
test_potrf(Uplo, N, (TYPE*)(wrksets+i*setsz), lda);
}
t1 = time00();
free(wrksets);
return((t1-t0)/((double)nrep));
}
static TYPE llttest(enum ATLAS_UPLO Uplo, int CacheSize, int N, int lda,
double *tim)
{
TYPE *A, *LmLt;
int i;
double t0, t1;
TYPE normA, eps, resid;
eps = Mjoin(PATL,epsilon)();
A = malloc(ATL_MulBySize(lda)*N);
if (A == NULL) return(-1);
t0 = ATL_flushcache(CacheSize);
lltgen(Uplo, N, A, lda, N*1029+lda);
normA = lltnrm1(Uplo, N, A, lda);
#ifdef DEBUG
Mjoin(PATL,geprint)("A0", N, N, A, lda);
#endif
t0 = ATL_flushcache(-1);
t0 = time00();
test_potrf(Uplo, N, A, lda);
t1 = time00() - t0;
*tim = t1;
t0 = ATL_flushcache(0);
#ifdef DEBUG
Mjoin(PATL,geprint)("L", N, N, A, lda);
#endif
ATL_checkpad(Uplo, N, A, lda);
if (Uplo == AtlasUpper) LmLt = ATL_UtmulU(N, A, lda);
else LmLt = ATL_LmulLt(N, A, lda);
#ifdef DEBUG
Mjoin(PATL,geprint)("L*Lt", N, N, LmLt, N);
#endif
lltgen(Uplo, N, A, lda, N*1029+lda); /* regen A over LLt */
lltdiff(Uplo, N, A, lda, LmLt, N);
#ifdef DEBUG
Mjoin(PATL,geprint)("A-L*Lt", N, N, LmLt, N);
#endif
resid = lltnrm1(Uplo, N, LmLt, N);
#ifdef DEBUG
if (resid/(normA*eps*N) > 10.0)
fprintf(stderr, "normA=%e, eps=%e, num=%e\n", normA, eps, resid);
#endif
resid /= (normA * eps * N);
free(LmLt);
free(A);
return(resid);
}
int mmcase0(int MFLOP, int CACHESIZE, char TA, char TB, int M, int N, int K,
SCALAR alpha, int lda, int ldb, SCALAR beta, int ldc)
{
char *pc;
#ifdef TREAL
char *form="%4d %c %c %4d %4d %4d %5.1f %5.1f %6.2f %5.1f %5.2f %3s\n";
#define MALPH alpha
#define MBETA beta
TYPE betinv, bet=beta;
#else
#define MALPH *alpha, alpha[1]
#define MBETA *beta, beta[1]
char *form="%4d %c %c %4d %4d %4d %5.1f %5.1f %5.1f %5.1f %6.2f %6.1f %4.2f %3s\n";
TYPE betinv[2], *bet=beta;
#endif
int nreps, incA, incB, incC, inc, nmat, k;
TYPE *c, *C, *a, *A, *b, *B, *st;
int ii, jj, i, j=0, PASSED, nerrs;
double t0, t1, t2, t3, mflop, mf, mops;
TYPE maxval, f1, ferr;
static TYPE feps=0.0;
static int itst=1;
enum ATLAS_TRANS TAc, TBc;
void *vp;
#ifdef TCPLX
if (*beta == 0.0 && beta[1] == 0.0) betinv[0] = betinv[1] = 0.0;
else if (beta[1] == 0.0) { betinv[0] = 1 / *beta; betinv[1] = 0.0; }
else
{
t0 = *beta;
t1 = beta[1];
if (Mabs(t1) <= Mabs(t0))
{
t2 = t1 / t0;
betinv[0] = t0 = 1.0 / (t0 + t1*t2);
betinv[1] = -t0 * t2;
}
else
{
t2 = t0 / t1;
betinv[1] = t0 = -1.0 / (t1 + t0*t2);
betinv[0] = -t2 * t0;
}
}
mops = ( ((8.0*M)*N)*K ) / 1000000.0;
#else
if (beta != 0.0) betinv = 1.0 / beta;
else betinv = beta;
mops = ( ((2.0*M)*N)*K ) / 1000000.0;
#endif
nreps = MFLOP / mops;
if (nreps < 1) nreps = 1;
if (TA == 'n' || TA == 'N')
{
TAc = AtlasNoTrans;
incA = lda * K;
}
else
{
if (TA == 'c' || TA == 'C') TAc = AtlasConjTrans;
else TAc = AtlasTrans;
incA = lda * M;
}
if (TB == 'n' || TB == 'N')
{
incB = ldb * N;
TBc = AtlasNoTrans;
}
else
{
incB = ldb * K;
if (TB == 'c' || TB == 'C') TBc = AtlasConjTrans;
else TBc = AtlasTrans;
}
incC = ldc*N;
inc = incA + incB + incC;
i = M*K + K*N + M*N; /* amount of inc actually referenced */
/* This is a hack; change to use of flushcache instead. */
nmat = ((CACHESIZE/ATL_sizeof) + i)/i;
vp = malloc(ATL_MulBySize(nmat*inc)+ATL_Cachelen);
ATL_assert(vp);
C = c = ATL_AlignPtr(vp);
a = A = C + incC;
b = B = A + incA;
st = C + nmat*inc;
matgen(inc, nmat, C, inc, M*N);
#ifdef DEBUG
printmat("A0", M, K, A, lda);
printmat("B0", K, N, B, ldb);
printmat("C0", M, N, C, ldc);
#endif
t0 = time00();
for (k=nreps; k; k--)
{
trusted_gemm(TAc, TBc, M, N, K, alpha, a, lda, b, ldb, bet, c, ldc);
c += inc; a += inc; b += inc;
if (c == st)
{
c = C; a = A; b = B;
if (bet == beta) bet = betinv;
else bet = beta;
}
}
t1 = time00() - t0;
t1 /= nreps;
if (t1 <= 0.0) mflop = t1 = 0.0;
else /* flop rates actually 8MNK+12MN & 2MNK + 2MN, resp */
mflop = mops / t1;
printf(form, itst, TA, TB, M, N, K, MALPH, MBETA, t1, mflop, 1.0, "---");
#ifdef DEBUG
printmat("C", M, N, C, ldc);
#endif
matgen(inc, nmat, C, inc, M*N);
t0 = time00();
for (k=nreps; k; k--)
{
test_gemm(TAc, TBc, M, N, K, alpha, a, lda, b, ldb, bet, c, ldc);
c += inc; a += inc; b += inc;
if (c == st)
{
c = C; a = A; b = B;
if (bet == beta) bet = betinv;
else bet = beta;
}
}
t2 = time00() - t0;
t2 /= nreps;
if (t2 <= 0.0) t2 = mflop = 0.0;
else mflop = mops / t2;
pc = "---";
if (t1 == t2) t3 = 1.0;
else if (t2 != 0.0) t3 = t1/t2;
else t3 = 0.0;
printf(form, itst++, TA, TB, M, N, K, MALPH, MBETA, t2, mflop, t3, pc);
free(vp);
return(1);
}
int mmcase(int TEST, int CACHESIZE, char TA, char TB, int M, int N, int K,
SCALAR alpha, TYPE *A, int lda, TYPE *B, int ldb, SCALAR beta,
TYPE *C, int ldc, TYPE *D, int ldd)
{
char *pc;
#ifdef TREAL
char *form="%4d %c %c %4d %4d %4d %5.1f %5.1f %6.2f %5.1f %5.2f %3s\n";
#define MALPH alpha
#define MBETA beta
#else
#define MALPH *alpha, alpha[1]
#define MBETA *beta, beta[1]
char *form="%4d %c %c %4d %4d %4d %5.1f %5.1f %5.1f %5.1f %6.2f %6.1f %4.2f %3s\n";
#endif
int ii, jj, i, j=0, PASSED, nerrs;
double t0, t1, t2, t3, mflop;
TYPE maxval, f1, ferr;
static TYPE feps=0.0;
static int itst=1;
/*int *L2, nL2=(1.3*L2SIZE)/sizeof(int);*/
enum ATLAS_TRANS TAc, TBc;
double l2ret;
if (!TEST) D = C;
/*if (nL2) L2 = malloc(nL2*sizeof(int));*/
l2ret = ATL_flushcache( CACHESIZE );
if (TA == 'n' || TA == 'N')
{
matgen(M, K, A, lda, K*1112);
TAc = AtlasNoTrans;
}
else
{
matgen(K, M, A, lda, K*1112);
if (TA == 'c' || TA == 'C') TAc = AtlasConjTrans;
else TAc = AtlasTrans;
}
if (TB == 'n' || TB == 'N')
{
matgen(K, N, B, ldb, N*2238);
TBc = AtlasNoTrans;
}
else
{
matgen(N, K, B, ldb, N*2238);
if (TB == 'c' || TB == 'C') TBc = AtlasConjTrans;
else TBc = AtlasTrans;
}
matgen(M, N, C, ldc, M*N);
#ifdef DEBUG
printmat("A0", M, K, A, lda);
printmat("B0", K, N, B, ldb);
printmat("C0", M, N, C, ldc);
#endif
/*
if (L2)
{
for (i=0; i != nL2; i++) L2[i] = 0.0;
for (i=0; i != nL2; i++) j += L2[i];
}*/
/* invalidate L2 cache */
l2ret = ATL_flushcache( -1 );
t0 = time00();
trusted_gemm(TAc, TBc, M, N, K, alpha, A, lda, B, ldb, beta, C, ldc);
t1 = time00() - t0;
if (t1 <= 0.0) mflop = t1 = 0.0;
else /* flop rates actually 8MNK+12MN & 2MNK + 2MN, resp */
#ifdef TCPLX
mflop = ( ((8.0*M)*N)*K ) / (t1*1000000.0);
#else
mflop = ( ((2.0*M)*N)*K ) / (t1*1000000.0);
#endif
printf(form, itst, TA, TB, M, N, K, MALPH, MBETA, t1, mflop, 1.0, "---");
#ifdef DEBUG
printmat("C", M, N, C, ldc);
#endif
#ifndef TIMEONLY
matgen(M, N, D, ldd, M*N);
/* invalidate L2 cache */
l2ret = ATL_flushcache( -1 );
t0 = time00();
test_gemm(TAc, TBc, M, N, K, alpha, A, lda, B, ldb, beta, D, ldd);
t2 = time00() - t0;
if (t2 <= 0.0) t2 = mflop = 0.0;
else
#ifdef TCPLX
mflop = ( ((8.0*M)*N)*K ) / (t2*1000000.0);
#else
mflop = ( ((2.0*M)*N)*K ) / (t2*1000000.0);
#endif
#ifdef DEBUG
printmat("D", M, N, D, ldd);
#endif
if (TEST)
{
if (feps == 0.0)
{
#if 0
f1 = feps = 0.5;
do
{
feps = f1;
f1 *= 0.5;
maxval = 1.0 + f1;
}
while (maxval != 1.0);
printf("feps=%e\n",feps);
#else
feps = EPS;
#endif
#ifdef DEBUG
printf("feps=%e\n",feps);
#endif
}
#ifdef TREAL
ferr = 2.0 * (Mabs(alpha) * 2.0*K*feps + Mabs(beta) * feps) + feps;
#else
f1 = Mabs(*alpha) + Mabs(alpha[1]);
maxval = Mabs(*beta) + Mabs(beta[1]);
ferr = 2.0 * (f1*8.0*K*feps + maxval*feps) + feps;
#endif
PASSED = 1;
maxval = 0.0;
pc = "YES";
nerrs = ii = jj = 0;
for (j=0; j != N; j++)
{
for (i=0; i != M SHIFT; i++)
{
f1 = D[i] - C[i];
if (f1 < 0.0) f1 = -f1;
if (f1 > ferr)
{
nerrs++;
PASSED = 0;
pc = "NO!";
if (f1 > maxval)
{
maxval=f1;
ii = i+1;
jj = j+1;
}
}
}
D += ldd SHIFT;
C += ldc SHIFT;
}
if (maxval != 0.0)
fprintf(stderr, "ERROR: nerr=%d, i=%d, j=%d, maxval=%e\n", nerrs, ii,jj, maxval);
}
else pc = "---";
if (t1 == t2) t3 = 1.0;
else if (t2 != 0.0) t3 = t1/t2;
else t3 = 0.0;
printf(form, itst++, TA, TB, M, N, K, MALPH, MBETA, t2, mflop, t3, pc);
#else
itst++;
PASSED = 1;
#endif
/*free(L2);*/
l2ret = ATL_flushcache( 0 );
return(PASSED);
}
int RunCase(int CacheSize, TYPE thresh, int MFLOP, enum ATLAS_ORDER Order,
int M, int N, int lda)
{
char *cord = (Order == AtlasColMajor ? "Col" : "Row");
const double maxMN = Mmax(M,N), minMN = Mmin(M,N);
unsigned long nreps=0;
int npiv=(-1), *ipiv;
const int incA = (Order == AtlasColMajor ? N*lda : M*lda);
double mflops, mflop, resid, tim=(-1.0), t0;
TYPE *A, *a;
int i;
#ifdef TREAL
mflops = maxMN * minMN * minMN - ((minMN*minMN*minMN) / 3.0) -
(minMN*minMN) / 2.0;
#else
mflops = (maxMN * minMN * minMN - ((minMN*minMN*minMN) / 3.0) +
(maxMN*minMN) / 2.0)*4.0 - 3.0 * minMN*minMN;
#endif
mflops /= 1000000.0;
if (thresh > ATL_rzero)
{
if (Order == AtlasColMajor)
resid = lutestC(CacheSize, M, N, lda, &npiv, &tim);
else resid = lutestR(CacheSize, M, N, lda, &npiv, &tim);
}
else resid = -1.0;
if (MFLOP > mflops || thresh <= ATL_rzero) /* need to time repetitively */
{
nreps = (mflops*1000000);
nreps = (MFLOP*1000000 + nreps-1) / nreps;
if (nreps < 1) nreps = 1;
i = ATL_DivBySize(2*CacheSize) ATL_PTCACHEMUL;
i = (i + M*N) / (M*N);
if (i < nreps) i = nreps; /* don't reuse mem or no pivoting */
a = A = malloc(i * ATL_MulBySize(incA));
if (A != NULL)
{
ipiv = malloc(Mmin(M,N)*sizeof(int)); /* what the hell - reuse ipiv */
if (ipiv)
{
Mjoin(PATL,gegen)(i*incA, 1, A, i*incA, incA+M+3012);
t0 = time00();
for (i=nreps; i; i--, a += incA)
test_getrf(Order, M, N, a, lda, ipiv);
tim = time00() - t0;
tim /= nreps;
if (npiv == 0) npiv = findnpvt(Mmin(M,N), ipiv);
free(ipiv);
}
else fprintf(stderr, " WARNING: not enough mem to run timings!\n");
free(A);
}
else fprintf(stderr, " WARNING: not enough mem to run timings!\n");
}
if (tim > 0.0) mflop = mflops / tim;
else mflop = 0.0;
fprintf(stdout, "%5d %3s %6d %6d %6d %6d %9.3f %9.3f %9.3e\n",
nreps, cord, M, N, lda, npiv, tim, mflop, resid);
return(resid <= thresh);
}
double gemvcase(const int MFLOP, const enum ATLAS_TRANS TA, const int l2size,
const int M, const int N, const SCALAR alpha, const int lda,
const SCALAR beta)
{
unsigned long reps;
int i, lx, ly, la;
#ifdef TREAL
const double flops = 2.0 * M * N;
#else
const double flops = 8.0 * M * N;
#endif
double ttest, mftest, t0;
const int aincY=1, aincX=1, incY=1, incX=1;
const int inca = (TA == AtlasNoTrans) ? lda * (N SHIFT) : lda * (M SHIFT);
const int incx = N*incX SHIFT, incy = M*incY SHIFT;
TYPE *a, *A, *stA, *A0, *x, *X, *X0, *stX, *y, *Y, *Y0, *stY;
#ifdef TREAL
const TYPE nbeta = -beta;
TYPE bet = beta;
#else
const TYPE *bet = beta;
TYPE nbeta[2];
nbeta[0] = -beta[0]; nbeta[1] = -beta[1];
#endif
i = (ATL_DivBySize(l2size)+N-1)/N;
if (i < 1) i = 1;
lx = i * N * aincX;
X0 = X = x = malloc(ATL_MulBySize(lx));
if (x == NULL) return(-1);
i = (ATL_DivBySize(l2size)+M-1)/M;
if (i < 1) i = 1;
ly = i * M * aincY;
Y0 = Y = y = malloc(ATL_MulBySize(ly));
if (y == NULL)
{
free(x);
return(-1);
}
i = (ATL_DivBySize(l2size)+M*N)/(M*N);
la = i * inca;
A0 = A = a = malloc(ATL_MulBySize(la));
if (a == NULL)
{
free(x);
free(y);
return(-1);
}
if (incX < 1)
{
stX = x;
x = X = x + (lx SHIFT);
}
else stX = x + (lx SHIFT);
if (incY < 1)
{
stY = y;
y = Y = y + (ly SHIFT);
}
else stY = y + (ly SHIFT);
stA = a + (la SHIFT);
reps = (MFLOP * 1000000.0) / flops;
if (reps < 1) reps = 1;
Mjoin(PATL,gegen)(ly, 1, Y0, ly, M*incY);
Mjoin(PATL,gegen)(lx, 1, X0, lx, N*incY+127*50+77);
Mjoin(PATL,gegen)(la, 1, A0, la, N*M+513*7+90);
t0 = time00();
for (i=reps; i; i--)
{
#ifdef SYMM_
Mjoin(PATL,symv)(AtlasLower, N, alpha, a, lda, x, incX, beta, y, incY);
#else
Mjoin(PATL,gemv)(TA, M, N, alpha, a, lda, x, incX, beta, y, incY);
#endif
x += incx;
y += incy;
a += inca;
if (x == stX) x = X;
if (y == stY)
{
y = Y;
if (bet == beta) bet = nbeta;
else bet = beta;
}
if (a == stA) a = A;
}
ttest = time00() - t0;
if (ttest > 0.0) mftest = (reps * flops) / (1000000.0 * ttest);
else mftest = 0.0;
free(A0);
free(X0);
free(Y0);
return(mftest);
}
double GetTimeWithReps_QL
(int mflopF, int lda, int M, int N, int nb, int Uplo, int Side, int flsizeKB)
{
double mflop, t0, t1, drep;
TYPE dtmp, dtmp1;
char *wrksets; /* working sets for kernel calls */
#ifdef TCPLX
const int lda2 = lda+lda;
#else
const int lda2 = lda;
#endif
size_t setsz, setszT; /* work set size in memory, and amnt of it touched */
size_t nrep; /* # of reps required to force mflopF flops */
size_t nset; /* # of working sets allocated */
int wlen; /* length of QR's workspace */
int i;
/*
* Figure out how much workspace is required, and allocate it
*/
test_geqlf(CblasColMajor, M, N, &dtmp1, lda, &dtmp1, &dtmp, -1);
wlen = dtmp;
/*
* QR accesses matrix, Min(M,N)-length tau & workspace, but for flush purposes
* be conservative and say it only accesses A
*/
setsz = (lda*N + wlen + Mmin(M,N)) * ATL_sizeof;
setszT = M*N*ATL_sizeof;
mflop = GetFlopCount(LAgeqrf, LARight+LALower, M, N, 0, 0, CAN_NB);
/*
* Cannot reuse matrices (bogus to factor an already factored matrix), so we
* must take as our total memspace MAX(nrep,nset)*setsz
*/
ATL_assert(mflop > 0.0);
drep = (mflopF*1.0e6) / mflop;
nrep = (int)(drep+0.999999);
/*
* If cacheline flush doesn't work, then we must use this method
*/
#if ATL_LINEFLUSH
if (nrep < 2)
return(-1.0); /* do wt normal timer */
#else
nrep = (nrep >= 1) ? nrep : 1;
#endif
nset = (flsizeKB*1024+setszT-1)/setszT;
if (nset < nrep)
nset = nrep;
wrksets = malloc(nset * setsz);
ATL_assert(wrksets);
for (i=0; i < nset; i++)
Mjoin(PATL,gegen)(M, N, (TYPE*)(wrksets+i*setsz), lda, M*N+lda);
t0 = time00();
for (i=0; i < nrep; i++)
{
test_geqlf(CblasColMajor, M, N, (TYPE*)(wrksets+i*setsz), lda,
(TYPE*)(wrksets+i*setsz+(N*lda+wlen)*ATL_sizeof),
(TYPE*)(wrksets+i*setsz+N*lda*ATL_sizeof), wlen);
}
t1 = time00();
free(wrksets);
return((t1-t0)/((double)nrep));
}
double GetTime(int rout, int mflopF, int lda, int M, int N, int nb, int Uplo,
int Side, int flsizeKB)
{
#if ATL_LINEFLUSH
FLSTRUCT *flp;
#endif
TYPE *A, *wrk=NULL, dtmp, dtmp1, *tau=NULL;
int *ipiv=NULL, itmp, wlen;
double t0, t1;
/*
* Call routs that force particular flop count if requested; they return -1.0
* if one invocation will suffice to force mflopF, in which case do the timing
* in this routine, which is simpler & doesn't require LRU & as much workspace
* If we don't have the ability to do cacheline flushing, must use LRU rout!
*/
#if ATL_LINEFLUSH
if (mflopF > 0)
{
#endif
if (rout == LApotrf)
t1 = GetTimeWithReps_LLT(mflopF, lda, M, N, nb, Uplo, Side, flsizeKB);
else if (rout == LAgeqrf)
{
if (Side == LARight)
{
if (Uplo == LAUpper)
t1 = GetTimeWithReps_QR(mflopF, lda, M, N, nb, Uplo, Side,
flsizeKB);
else
t1 = GetTimeWithReps_QL(mflopF, lda, M, N, nb, Uplo, Side,
flsizeKB);
}
else if (Uplo == LAUpper)
t1 = GetTimeWithReps_RQ(mflopF, lda, M, N, nb, Uplo, Side,
flsizeKB);
else
t1 = GetTimeWithReps_LQ(mflopF, lda, M, N, nb, Uplo, Side,
flsizeKB);
}
else
t1 = GetTimeWithReps_LU(mflopF, lda, M, N, nb, Uplo, Side, flsizeKB);
#if ATL_LINEFLUSH == 0
return(t1);
#else
if (t1 >= 0.0)
return(t1);
}
#endif
#if ATL_LINEFLUSH != 0
/*
* Generate operands
*/
A = GetGE(M, N, lda);
ATL_assert(A);
flp = ATL_GetFlushStruct(A, N*((size_t)lda)*ATL_sizeof, NULL);
if (rout == LApotrf)
PosDefGen(CblasColMajor, Uplo_LA2ATL(Uplo), N, A, lda);
else if (rout & LAgeqrf)
{ /* QR must allocate workspace */
if (Side == LARight)
{
if (Uplo == LAUpper)
{
test_geqrf(CblasColMajor, M, N, A, lda, &dtmp1, &dtmp, -1);
}
else
{
test_geqlf(CblasColMajor, M, N, A, lda, &dtmp1, &dtmp, -1);
}
}
else if (Uplo == LAUpper)
{
test_gerqf(CblasColMajor, M, N, A, lda, &dtmp1, &dtmp, -1);
}
else
{
test_gelqf(CblasColMajor, M, N, A, lda, &dtmp1, &dtmp, -1);
}
wlen = dtmp;
wrk = calloc(wlen, ATL_sizeof);
ATL_assert(wrk);
flp = ATL_GetFlushStruct(wrk, wlen*ATL_sizeof, flp);
itmp = (M >= N) ? M : N;
tau = calloc(itmp, ATL_sizeof);
flp = ATL_GetFlushStruct(tau, itmp*ATL_sizeof, flp);
}
else
{
ipiv = calloc(M, sizeof(int));
ATL_assert(ipiv);
flp = ATL_GetFlushStruct(ipiv, M*sizeof(int), flp);
}
/*
* Flush cache, and do timing
*/
ATL_FlushAreasByCL(flp);
if (rout == LApotrf)
{
t0 = time00();
test_potrf(Uplo, N, A, lda);
t1 = time00();
}
else if (rout == LAgeqrf)
{
if (Side == LARight)
{
if (Uplo == LAUpper)
{
t0 = time00();
test_geqrf(CblasColMajor, M, N, A, lda, tau, wrk, wlen);
t1 = time00();
}
else
{
t0 = time00();
test_geqlf(CblasColMajor, M, N, A, lda, tau, wrk, wlen);
t1 = time00();
}
}
else if (Uplo == LAUpper)
{
t0 = time00();
test_gerqf(CblasColMajor, M, N, A, lda, tau, wrk, wlen);
t1 = time00();
}
else
{
t0 = time00();
test_gelqf(CblasColMajor, M, N, A, lda, tau, wrk, wlen);
t1 = time00();
}
}
else
{
t0 = time00();
test_getrf(CblasColMajor, M, N, A, lda, ipiv);
t1 = time00();
}
if (tau)
free(tau);
if (wrk)
free(wrk);
if (ipiv)
free(ipiv);
free(A);
ATL_KillAllFlushStructs(flp);
return(t1 - t0);
#endif
}
static TYPE trtritest(enum ATLAS_ORDER Order, enum ATLAS_UPLO Uplo,
enum ATLAS_DIAG Diag, int CacheSize, int N, int lda,
double *tim)
{
TYPE *A, *Acompare;
int i;
double t0, t1;
TYPE normA, eps, resid;
/*int ierr;*/
#ifdef TCPLX
const TYPE one[2]={ATL_rone, ATL_rzero};
#else
const TYPE one = ATL_rone;
#endif
eps = Mjoin(PATL,epsilon)();
A = malloc(ATL_MulBySize(lda)*N);
Acompare = malloc(ATL_MulBySize(lda)*N);
if (A == NULL) return(-1);
if (Acompare == NULL) return(-1);
t0 = ATL_flushcache(CacheSize);
/* create random, diagonally dominant matrix with magic value at
unused places. Last number is just the random seed. */
trigen(Order, Uplo, Diag, N, A, lda, PADVAL, N*1029+lda);
/* Create backup to calculate residual. This one has to be used
as a full matrix, so it has zero fills and correct diagonal. */
trigen(Order, Uplo, Diag, N, Acompare, lda, ATL_rzero, N*1029+lda);
if (Diag==AtlasUnit)
for (i=0; i < N; i++)
Acompare[(i*(lda+1)) SHIFT] = ATL_rone;
normA = trinrm1(Order,Uplo, Diag, N, A, lda);
#ifdef DEBUG
Mjoin(PATL,geprint)("A0", N, N, A, lda);
#endif
t0 = ATL_flushcache(-1);
/* Calculate and time a solution */
t0 = time00();
test_trtri(Order, Uplo, Diag, N, A, lda);
t1 = time00() - t0;
*tim = t1;
/* if (ierr != 0)
{
fprintf(stderr, "Return values != 0 : %d \n",ierr);
return(9999.9999);
}*/
t0 = ATL_flushcache(0);
/* Instroduce a padding error. */
/* A[(5+5*lda)SHIFT]=114.0; */
#ifdef DEBUG
Mjoin(PATL,geprint)("L", N, N, A, lda);
#endif
ATL_checkpad(Order, Uplo, Diag, N, A, lda);
/* Calculate A^{-1}*A */
cblas_trmm(Order,CblasLeft,Uplo,AtlasNoTrans,Diag,
N,N,one,A,lda,Acompare,lda);
#ifdef DEBUG
Mjoin(PATL,geprint)("A^{-1}*A", N, N, Acompare, N);
#endif
/* Subtract diagonal */
for (i=0; i < N; i++)
Acompare[i*((lda+1) SHIFT)] -= ATL_rone;
/*
resid = trinrm1(Order, Uplo,AtlasNonUnit,N,Acompare,lda);
fprintf(stderr, "normA=%e, eps=%e, num=%e\n", normA, eps, resid);
*/
resid = Mjoin(PATL,genrm1)(N, N, Acompare, lda);
#ifdef DEBUG
if (resid/(normA*eps*N) > 10.0)
fprintf(stderr, "normA=%e, eps=%e, num=%e\n", normA, eps, resid);
#endif
resid /= (normA * eps * N);
free(Acompare);
free(A);
return(resid);
}